Since Nikola Tesla performed the resonant coil experiments in 1891 and many scientists followed the suit, the working theory and the possibility of using electromagnetic resonant coil for wireless energy transmission have been widely validated. Based on the electromagnetic resonance wireless energy transmission theory, many applications are also developed, such as, resonant transformers, RF battery recharger and RFID system, and so on. These systems have been widely applied to many practical fields.
FIG. 1 shows a schematic view of a conventional one-to-one wireless energy transmission system. As shown in FIG. 1, a transmission driver circuit 102 receives energy from an energy source 101 to drive the coil of a resonance transmission circuit 103. Take the circular transmission coil as example. The characteristic dimension of the coil can be expressed by the radius r. The characteristic dimension of transmission coils of other form can be expressed with other parameters. The transmission coil generates a periodic magnetic field with frequency f0 in the space. A resonance receiving circuit 104 is placed at a distance d from resonance transmission circuit 103. Resonance receiving circuit 104 includes receiving coil tuned to the resonance frequency f0 in order to receive the periodic magnetic field from the space with the optimal coupling efficiency. The received energy, after deducting the loss by a redundant energy consumption circuit 105, is transformed into the energy source for a subsequent energy consumption circuit 106 of resonance receiving circuit 104. To ensure the system applicability and preferred coupling efficiency, both the transmission coil and receiving coil are usually designed with a small dimension so that the magnetic field has a stronger concentration with specific directivity. Furthermore, the transmission coil and the receiving coil have the similar characteristic dimension and have a higher Q value.
As the understanding of electromagnetic wireless energy transmission spreads, more applications or experimental improvements are proposed. For example, much effort is devoted to the development of a one-to-many wireless energy transmission system so that the system can transmit energy wirelessly to a plurality of receivers within a specific working range, such as, 1 meter, to function normally.
However, for a feasible one-to-many wireless energy transmission system, the system must meet the following criteria:                1. The coverage area or volume of generated magnetic field must have a sufficiently large work range to accommodate at least the maximum number of receivers allowed by the system definition.        2. The generated magnetic field must be sufficiently uniform in every direction and point with the work range so that each of the receivers within the work range is able to absorb energy sufficient to maintain functioning normally.        3. Each of the receivers within the work range must be able to function independently and without interference with each other.        
To meet the aforementioned criteria, a conventional approach is to create a system based on the conventional one-to-one system shown in FIG. 1 and then increase the transmission energy to generate a more intensive magnetic field. Nevertheless, this approach will incur at least the following problems.
The first problem is the uniformity of the magnetic field. Based on the wireless energy transmission theory, as shown in FIG. 2, an inverse cube law exists between the magnetic field density (B) and the coupling distance (d) along the direction perpendicular to the transmission coil, while an inverse square law exists between the magnetic field density and the coupling distance along the direction parallel to the transmission coil. Both the inverse cube law and the inverse square law indicate that the magnetic field density will decay rapidly as the coupling distance increases. Although the transmission coil and receiving coil with high Q value can attract more magnetic lines passing through the coils, i.e., receiving more energy, the received energy will still decay greatly as the coupling distance increases. That is, the coupling efficiency relies greatly on the coupling distance. In other words, the magnetic field distribution is very non-uniform. In this type of system configuration, the transmission energy must be very large for the receiver with the largest distance defined by the system to receive sufficient minimum received energy defined by the system. On the other hand, when the receiver is located at a distance less than the maximum distance defined by the system, the receiver will receive more energy than the defined minimum energy required to maintain normal functioning. The conventional approach is to design the receiver and related subsequent circuit to function normally when receiving only the defined minimum energy. Alternatively, because the related subsequent circuit of the receiver should not function differently for distances from the transmission coil, the excessive energy received by the receiver will be consumed via voltage clamping circuit or voltage regulator. For the energy efficiency issue, this approach is unnecessary waste of energy, which also lowers the overall efficiency of the system. On the other hand, the need to transmit a large amount of energy will increase the difficulty of transmission circuit design as well as the deployment and operation costs.
The second problem is related to the directivity of the magnetic field. Based on the wireless energy transmission theory, for a point with distance d from the physical center of the transmission coil, an inverse square law exists between the magnetic field density (B) and the characteristic dimension (r) of the transmission coil in the direction perpendicular to the transmission coil, while a positive proportional law exists between the magnetic field density (B) and the characteristic dimension (r) of the transmission coil in the direction parallel to the transmission coil. In other words, the transmission coil with a smaller characteristic dimension r will have a higher magnetic field dimension in the direction perpendicular to the transmission coil and a lower magnetic field dimension in the direction parallel to the transmission coil. That is, the transmission coil is more directional. This does not meet the aforementioned criteria because if all of the receivers must be located in the same direction with respect to the transmission coil, the receivers closer to the transmission coil will absorb a larger portion of the energy and prevent the receivers located further from receiving sufficient energy.
The third problem is related to the stability issue. For conventional one-to-one wireless energy transmission system, the design principle is to have transmission and resonance receiving circuits with high Q values so that the resonance receiving circuit can absorb as much transmitted energy as possible. However, if two receivers with high Q values are placed within the work range of a one-to-many wireless transmission system, these two receivers will compete for energy absorption, which leads to unstable operation. The usual outcome will be the receiver placed closer to the transmitter absorbs almost all the transmitted energy while the receiver placed further from the transmitter will absorb almost nothing. In other words, the receivers will interfere with each other. If more receivers are placed within the work range, the situation will become very complicated and some of the receivers may not be able to function because of other receivers. Hence, the design of making each of receivers having high Q value is only applicable to one-to-one transmission system, but not to one-to-many transmission system.
Therefore, the one-to-many wireless energy transmission system cannot be treated as a simple direct extension of a one-to-one wireless energy transmission system. The design of a stable one-to-many wireless energy transmission system is an important issue as well as the foundation of many more applications.